Hi Ernest,
I found this hinting for something else. And wanted to share it as see it might be something on your road map…
https://woocommerce.com/products/ajax-instant-search/
They have the short code for the menu.
Here’s an example of it in use
https://adasignfactory.com/product/lab-sign/
Still am curious about the “facets” in your screen shot but want to show you this because I feel like I don’t clearly describe what it is I’m talking about 🙂